Semiotics is the study of signs. Signs mediate meaning, and are not just simple "tokens" or physical marks; they can be complex combinations of other lower level signs, such as whole sentences, spoken or written, newspaper advertisements, whole books, etc. The American logician Charles Sanders Peirce (pronounced "purse") introduced the term "semiotics," and several of its basic ideas. In particular, he emphasized that meanings are not directly attached to words; instead, there are events (or processes or activities) of semiosis - i.e. occurrences of meaning - each involving a signifier (called the representamen by Peirce), a signified (an object of some kind - e.g. a concept), and an interpretant that links these two; these three things are often called the semiotic triad and occur wherever there is meaning. The interpretant is not given, but must be created, e.g. by a person. This sounds simple, but it is very different from more common and naive theories, as in the use of denotational semantics for programming languages, where we have a function from programs (which are signs) to their denotations (which are meanings), in general defined using higher functions on some rather abstract mathematical domains. Our everyday language about meaning are oriented towards a dyadic interpretation, often using metaphors from a family called "the container metaphor." For some examples, consider: "I get it", "What does that convey?", "That's an empty phrase", "Where is this going?"
The second main source of semiotics is the Swiss linguist Ferdinand de Saussure. In both traditions, signs can be anything that mediates meaning, including words, images, sounds, gestures, and objects. In the tradition of Saussure, every sign has:
Signifier: The letters 't-r-e-e'.Note that a "sign" is a particular combination of a signifier and a signified. The same concept could be indicated by other signifiers, and the same signifier could refer to other things; in each case, we would have a different sign. (This explanation augments that in the "Signs" chapter of Semiotics for Beginners, by Daniel Chandler.)
Signified: The concept of tree.
Peirce's definition of sign is better, though more complex, because it includes the relation between signifier and signified as an explict component; this can include the interpreter, the context of interpretation, and even the process of interpretation. One of the most important insights of Peirce, which does not often seem to be emphasized in the literature that discusses his work, is that meaning is relational, not just denotational, and in particular is generally highly dependent on context. In our application area of user interface design, the interpreter is of course the user (or designer). More detailed discussion appears in On Notation.
An important notion from semiotics is Peirce's three way classification of signs into symbols, icons, and indices. These concepts have many applications to user interface design; again see On Notation for details. You should carefully note that each of these three terms has a technical meaning that is not the same as its ordinary everyday meaning!
Saussure's most important idea is probably that signs come in systems, not just one by one. Another important insight of Saussure that, in my opinion, has not been sufficiently emphasized, is that sign systems are organized by systematic differences among signs; we can relate this to a famous saying of Gregory Bateson, that "information is a difference that makes a difference." Saussure's idea that signs come in systems is illustrated by examples like the vowel systems of various accents of the same language, and the tense systems for verbs in various languages. The vowel system example shows that the same sign system can be realized in different ways; we call these different models. The vowel system example also shows that two different models of the same sign system can have the same elements but use them in a different way; so it's how elements are used that makes the models different, not the elements themselves. Models of sign systems are not just sets, they are sets with some kind of structure; we will learn more about this later. Alphabets also provide good examples where the sets overlap; for example, the Greek, Roman and Cyrillic alphabets each have some tokens in common, though they may have different meanings; thus, "P" is in all three alphabets, but "P" in the Cyrillic alphabet corresponds to "R" in the Roman alphabet. This motivates the need for "signs" as tokens that come in systems and have an interpretation; they cannot be just tokens as such. We can also motivate the need for systems of signs by noting that a sign system with just one element cannot convey any information (more technically, this is because its Shannon information content is zero).
Algebraic semiotics attempts to combine the major insights of Peirce and Saussure (among others) into a precise formalism that can be applied to the practical engineering of sign systems, e.g., in user interface design. This involves a fundamental change in perspective, from the analytic perspective of traditional semiotics, to a synthetic perspective, which is concerned with construction rather than just analysis. One important insight that this formalism incorporates is that signs need not be the simple little things that we usually call "signs," but instead can be very complex, such as a book, or a series of books, or even a whole library; or a movie or series of movies, or the GUI to an operating system. It is the job of user interface designers to build (parts of) such systems. Another insight that algebraic semiotics pursues is the importance of studying errors, that is, badly designed sign systems, in order to better understand what it means for a sign system to be well designed. This is interest is illustrated in the exhibits of the UC San Diego Semiotic Zoo.
Algebraic semiotics views sign systems as abstract data types, because the same information can be represented in a variety of different ways; for example, dates, times, and sports scores, each have multiple representations. This leads naturally to the idea that representations are mappings between abstract data types, as illustrated in an informal way by the examples in the UCSD Semiotic Zoo, which show how the failure of a representation to properly preserve some structure results in its being a suboptimal representation.
Traditional semiotics seems to have a Platonistic bias, in assuming that signs (which, please recall, we take to include both token and meaning) have an existence which is independent of human beings. But here we take a quite different approach, in basing signs on human social activity. We claim that signs do not have meanings in themselves, but only have whatever meaning we give to them. Moreover, insofar as these meanings are shared, they are necessarily social, and Plato's ideal entities play no role in this. In the contemporary humanities, semiotics has achieved the status of a common language, almost as much as mathematics in the sciences.